The domain name system is going to be changing, as of March 24.
You can read at: https://www.auda.org.au/
It will be possible for there two new domain name suffixes, .id.au and .au
If I insert such a registered domain name, in InfinityFree, while creating a new account,
and having encountered [Create a Hosting Account\Domain Name<?>], will everything
work exactly the same, as before?
I think it will just work. Assuming all the regular registry systems are being set up (DNS, WHOIS, etc.) and it will be added to things like the Public Suffix List, you should be able to use your domain here as soon as you get it.